A379501 a(n) = (3/2)*A019565((2n-1)^2) - A019565(A001065((2n-1)^2)), where A019565 is the base-2 exp-function, and A001065 is the sum of proper divisors of n.

2, 16, 216, 422, 470, 51016, 5082, 4446, 864, 106688, 1301846, 880, 204182, 1985872, 236964, 646310, 1030, 176778, 2799756, 96178962, 563400, 62092576, 1566805968, 27274, 559406, -16252236, 1040774592, 263042394, 7794826, 115781204, 13256922, -16386856, -1230440, 376172, -67188814, 222905278, 13547232, 28352541646

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to sigma(n).

Formula

a(n) = A379496(A016754(n)) = A019565(1+A016754(n)) - A379495(A016754(n)).

a(n) = (3/2)*A019565(A016754(n)) - A379495(A016754(n)).

Prog

(PARI)
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A379501(n) = { my(osq=((2*n)-1)^2); ((3/2)*A019565(osq) - A019565(sigma(osq)-osq)); };

Crossrefs

Cf. A001065, A016754, A019565, A379495, A379496.

Cf. also A378231, A337339.

Sequence in context: A360939 A114531 A365585 * A012056 A062971 A267782

Adjacent sequences: A379498 A379499 A379500 * A379502 A379503 A379504

Keyword

sign

Author

Antti Karttunen, Jan 05 2025

Status

approved